Ind. Eng. Chem. Res. 1993,32, 3180-3183
3180
Modified Group Contribution Method for Predicting the Entropy of Vaporization at the Normal Boiling Point Peisheng Ma and Xingmin Zhao’ Department of Chemical Engineering, Tianjin University, Tianjin 300072, People’s Republic of China
A new group contribution method has been proposed which only requires the molecular structure to predict the entropy of vaporization at the normal boiling point. The 483 compounds used to determine the group increments include a wide variety of organic substances. The average prediction error of the new method for these compounds is 1.4%. An extensive comparison has been made between our method and previously proposed techniques, and the results show that the new method has wider applicability and higher accuracy. Introduction Entropy of vaporization at the normal boiling point is one of the important properties in chemical engineering for which numerous estimation techniques have been proposed. The simple Trouton’s rule expressed this property as a constant (Shinoda, 1978). Many other estimation techniques involved functions of critical temperature, critical pressure, and normal boiling point (Chen, 1965;Giacalone, 1951; Riedel, 1954). A recently developed method was group contribution (Hoshino et al., 1983). Among these techniques, the group contribution method can be expected to have the widest applicability and the highest reliability. However, although Hoshino et al.’s method (Hoshino et al., 1983) was presented for both hydrocarbons and nonhydrocarbons, as will be seen below, it fails in some compounds. The reason is the substances selected to develop their method were mainly hydrocarbons, and the group division was too simple. In this paper, a modified group contribution method will be proposed to predict the vaporization entropy at the normal boiling point for a wide variety of organic compounds with high accuracy.
not more accurate than, the best data calculated from vapor pressures. Since the necessary experimental volumetric behavior is often unavailable and the calculation approaches in the determination of enthalpy from vapor pressures are often not clearly described in many works, the data selected in this paper are mainly direct calorimetric values, which accounts for 387 of the 483 data used. These data were taken from the work of Majer and Svoboda (1985),in which the calorimetric data were systematically divided into five classes, A, B, C, D, and E, implying the errors of the data in each class were less than 0.25 % ,0.5 % , 1 % , 2 % , and 5 76, respectively. All data we used were in classes, A, B, C, and D. The other 96 data were taken from the work of Reid et al. (1987),which were from vapor pressures. The 483 compounds are divided into 13 categories as shown in Table I, covering a wide range of organic compounds. Any organic compounds are assumed to be composed of some groups in Table 11, whereas the increments determined are also listed. As can be seen, the group division is much more precise than that in Hoshino et al.’s work (Hoshino et al., 1983).
Discussion Proposed Method The new method is based on the following formula,
where ASvb stands for the vaporization entropy at the normal boiling point, while is the latent heat of vaporization at the same temperature and Tb is the normal boiling point. A in eq 1 is a constant, Ai is the increment of group i, and ni is the number of group i in the molecule concerned. The constant A and the group increments are determined by least-squares data regression from experimental values of 483 compounds. The experimental entropies or enthalpies of vaporization were determined in two ways: measured by calorimeter and calculated from vapor pressures. The calorimetric data at the normal boiling point, if they are not determined by extrapolation from other temperature point(s), can be very accurate (error less than 0.5%1. The data derived from vapor pressures, if the vapor pressure-temperature data have high quality and the volumetric properties of both vapor and liquid phases are appropriately taken into account, may reach an error of 0.5%-1% in the moderate-pressure region, 5-150 kPa (Majer and Svoboda, 1985). That means the high-quality calorimetric data are at least as good as, if 0888-5885/93/2632-3180$04.00/0
A summary of the prediction deviations of the proposed method for all 13 classes of compounds is presented in Table I. The average error through the 483 compounds is 1.45% with the maximum error of 11% for transperfluorotetralin. The alcohol and phenol category has the greatest average error of 3.1 5%. This can be ascribed to the special properties of these compounds, such as the strong hydrogen bond effects. Extensive comparisons were made between our method and previously proposed techniques. Since correspondingstate methods need critical constants, in Table I11 80 compounds with experimental critical constants were chosen from the 483 substances to compare the new method with three corresponding-state estimations. The average deviation of our method for the 80 compounds is only about half of those of the three corresponding-state methods. As for Hoshino et al.’s group contribution estimation, it was found that for some of the 483 compounds, such as CH3N03, the prediction cannot be carried out because of no necessarygroup increments, while for some other compounds as listed in Table IV, no reasonable results can be obtained. In Table V, only 455 of the 483 compounds with reasonable results calculated by Hoshino et al.’s method are involved. The average errors of our method and Hoshino et al.’s are 1.4% and 2.6%,respectively. 0 1993 American Chemical Society
Ind. Eng. Chem. Res.,Vol. 32, No. 12, 1993 3181 Table I. Summary of Estimation Errors of the New Method.
no. of compds within range of e8tn error, % class of compds alkanes
alkenes and alkynes cyclohydrocarbons aromatics halogen-contg compds alcohols and phenols aldehydes and ketones esters ethers multioxygen-contg compds oxygen-halogen-con& compds nitrogen-contg compds sulfur-contg compds total 0
no. of compds 60 25 29 31 77 35 25 26 52 20 11 29 35 483
0-1
26 8 21
17 58 6 9 18 21 8 5 21 21 284
1-2 16 4 6 7 11 7 11
2-3 5 8 2 4 5 5 2
4 24 3 2 7 7 122
4 2 2 4 6 54
4-5
3-4
5-10
3 1
4
1 1
2 2 6
4
7 2
1 2
1
1
2 3
1
2
1
3
3 1 16
24
2 1 18
average % error 1.2 2.5 0.8 1.5 0.8 3.1 1.5 1.3 1.2 2.7 2.0 1.6 0.9 1.4
The deviation of 1-pentyne is 10.1%. The deviation of trans-perfluorotetralin is 11%.
Table 11. Grow Increments mOUD S i . Jsmol-l.K-l
>c=o
-1.434 77 1.698 07 2.504 26 1.856 79 -2.480 46 1.061 75 0.043 78 0.727 24 1.700 36 1.604 07 0.700 34 -1.145 46 21.809 00 3.394 57
-NH2 -CN -NHNH-SH
5.656 73 1.674 11 13.564 20 0.989 87
-CH2 =CH-NH-
-S-
-0.437 44 -0.780 38 6.602 87 3.875 56
-CH3 >C< -OH -SH
-1.484 45 2.218 68 19.410 00 1.397 61
=CH-
-0.084 51
-CH3 =CH-F -I -CHO
-0.293 55 3.183 53 -0.508 72 -1.834 80 6.980 96 0.058 86
-CH3 >C< =C< IC-CFS 4"zCl -CHCl=cc12 >CBrXI-CHFCl -CF2Br >CHOH
o=c-o-c=o
group
S i , J-mol-1.K-1
Non-Ring Groups 0.186 56 -2.604 40 0.610 72 10.702 00 0.963 41 2.073 63 2.417 36 0.614 62 -0.204 56 1.081 67 0.000 01 -0.608 41 21.976 11 -coo6.8773 7 o=c-O-C =o 15.976 01 -NH3.862 98 -NHNHz 13.747 70 -NO2 3.473 83 -S2.399 61 Groups in Rings >CH0.579 66 =C< -0.895 22 =N10.122 50 -03.114 35 Groups Connected to Rings -CH20.031 76 -F -1.122 92 -Coo5.662 69 -CHr =CH2 =C= -CH2F -CF2-CHC12 >CCl-CH2Br -CH2I -CF2C1 -CFCl-CFCll3r 3COH
Groups in Aromatic Rings =C< 0.948 53 Groups Connected to Aromatic Rings -CHr 1.560 46 >C< 1.893 27 -3.098 45 -CF3 10.489 20 -OH -CH20H 18.072 30 -NH2 6.704 16 A = 86.9178
To test the applicability and reliability of the new method, 100 compounds other than the 483 which had been used in the data regression were calculated. The average absolute deviation is 2.2 5% ;they are listed in Table VI and Table VIII. It must be pointed out that acids and polyhydridic alcohols are not included in the 483 substances mentioned above, because these compounds possess such different properties that they cannot be predicted with the same group increments as those in Table 11. For example, the vaporization entropy of acid a t normal boiling point
PUP >CH=CH=CH -CHF2 >CF-ccl3 =CHCl CHBr-
-CHI-CFC12 -CHClBr -CHzOH -CHO
-0-O-CHZCH~OH >N="HZ -NO3
-cos >C
c=o
>N-
1.028 30 4.357 29 5.617 53
>CH-CF2 -NH2
2.044 83 7.786 73 3.463 78
>CH=C< -C1 -0-
1.18641 3.892 95 -0.793 79 5.296 35 6.078 15
-coo-
increases much more rapidly than those compounds in Table I as the carbon chain in the molecule becomes longer, as is shown in Figure 1. The incrementa in Table VI1 could be used to estimate these compounds. As is well-known, the contributions of the halogen atoms connected to the same carbon should not be simply added; therefore, the carbon and the halogen atom(@as a whole are considered to be a group in this work. Nevertheless, many incrementa of such groups cannot be determined for lack of necessary data. It is difficult to solve this problem unless more experimental data are available.
3182 Ind. Eng. Chem, Res., Vol. 32, No,12, 1003 Table 111. Comparison of the New Method with Three Corwrponding-StateTechnique6 average ?& error average 5% error no,of new no.of new class of comDounds comDds method Riedel Chen Vetere class of compounds compds method Riedel Chen Vetere chainhydrocarbons 20 2.2 1.0 0.7 0.8 oxygen-contgcompds 25 2.7 5.5 5.6 5.5 cyclic hydrocarbons 5 0.7 2.1 1.3 1.6 nitrogen-contgcompds 10 2.6 9.1 7.5 7.9 aromatics 7 1.4 0.2 0.5 0.5 sulfur-contgcompds 4 0.4 0.8 0.7 1.1 halogen-contg compds 9 0.7 1.8 1.3 1.3 total 80 2.0 3.5 3.2 3.3
Table IV. Estimation Results of the New Method and Hoshino et al.'s Method (1983) for Some Communds uvb,d,
comaound cyclohexene indan perfluorobenzene pentafluorotoluene chloropentafluorobenzene octafluorotoluene perfluoropropylcyclohexane cis-perfluorotetralin trans-perfluorotetralin perfluoroieobutylcyclohexane 2,3-dihydrothiophene 2,bdihydrothiophene
&%b.-,
cis-decahydronaphthalene trans-decahydronaphthalene
J-mol-l-K-l 85.51 87.87 89.96 88.97 88.85 86.97 87.00 85.44 86.50 86.81 86.26 88.07 83.88 83.60
new method
Table V. Comparison of the New Method with Hoshino et al.'s Method (1983) no. of average % error class of compds compds newmethod 1.2 alkanes 50 2.5 alkenes and alkynes 25 cyclohydrocarbons 24 0.7 aromatics 30 1.5 0.7 halogen-contg compds 69 alcohola and phenols 35 3.1 1.5 aldehydes and alkones 25 1.3 esters 26 1.2 ethers 52 18 2.5 multi-oxygen-contgcompds 2.0 oxygen-halogen-contg compds 11 1.6 nitrogen-contg compds 64 0.9 sulfw-contg compds 29 total 455 1.4
Hoshino 0.5 2.8 0.8 2.8 2.0 4.5 3.1 2.1 1.9 5.9 3.1 4.8 1.1 2.6
J-mol-1.K-1 Hoshino 166.00 171.76 2.92 7.75 9.58 8.97 3.93 -79.65 -79.65 4.98 169.90 169.90 3.07 3.07
A%b,d~vbd
new method 0.99 1.01 1.00 1.00 1.00 1.00 1.00
Hoshino 0.52
0.51 30.81 11.48 9.27 9.70 22.14 ? ?
1.11
1.12 1.00 0.98 1.00 0.99 0.99
17.43 0.51 0.52 27.32 27.23
I
*y
0
- 0,-.m I
~
'4
~
n-alkanes
P i o -
co
D
>
w
n
Q
0 W
-
~
Table VI. Estimation Errors for Twelve Compounds Not Used in the Data Regression compound CiaHze C~H&~H(OH)-C~HS 1-CBHi70H CHpCHOCH=CHz (CzHahNH c2H,Ci CHzClCHClCHa CaHaBr CHaSCH(CH& CzH&(CHa)CzHa
relative % error new method Hoshino -3.5 1.3 -4.2 2.0 5.6 14.5 -0.8 1.6 -0.1 4.4 0.3 -3.6 0.8 0.6 -0.9 3.1 0.4
-0.2
CHI-CH,
-0.2 1.0
0.9 -0.5
CH2ClCH4Hz overall
-5.2 2.8
-6.3
'4
1
2
3
4
5
6
7
8
number of carbons Figure 1. Changes of as,b with carbon number in molecules. Table VII. Group Increments for Acids and Polyhydric Alcohols
-CHr >CH-CHa >CH-
Acids 15.056 -CH,16.994 -CObH Polyhydric Alcohols 18.295 CH2-11.267 -OH
15.750 -37.903 4.208 -3.120
Calculation Examples
3.3
Results A new group contribution method has been proposed which predicts the entropy of vaporization at the normal boiling point with wider applicability and higher accuracy than previous techniques.
The entropies of vaporization at the normal boiling point of l-methyl-l-ethylcyclopentane and naphthalene are calculated here to demonstrate how to use the newly proposed method. The experimental values of these compounds are obtained from the work of Majer and Svoboda (1985).
Ind. Eng.Chem. Res., Vol. 32,No. 12, 1993 3183 Table VIII. Prediction Results for Compounds Not Used in the Data Regression no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
exptl data, calcd data, compound J-mol-1-K-1 J-mol-1.K-1 84.28 2-methyloctane 86.69 86.49 84.28 3-methyloctane 4-methyloctane 86.14 84.28 3-ethylheptane 86.02 84.28 84.28 4-ethylheptane 84.92 2,2-dimethylheptane 85.26 83.62 85.35 84.28 2,3-dimethylheptane 85.96 84.28 2,4-dimethylheptane 85.78 84.28 2,5-dimethylheptane 85.96 84.28 2,6-dimethylheptane 3,3-dimethylheptane 84.84 83.62 85.31 84.28 3,4-dimethylheptane 84.28 3,5-dmethylheptane 85.78 83.62 84.72 4,4-dimethylheptane 83.81 86.49 2,2-dimethyloctane 84.67 86.40 2,3-dimethyloctane 84.67 2,4dimethyloctane 86.93 84.67 86.65 2,bdimethyloctane 84.67 86.97 2,6-dimethyloctane 84.67 87.07 2,7-dimethyloctane 83.81 85.89 3,3-dimethyloctane 84.67 86.37 3,4-dimethyloctane 84.67 86.47 3,5-dimethyloctane 83.85 84.71 cycloheptane 83.42 84.61 cyclooctane 83.23 83.98 1,l-dimethylcyclopentane 83.80 85.05 cis-1,2-dimethylcyclopentane 83.80 trans-1,2-dimethylcyclopentane 84.54 83.80 84.41 trans-1,3-dmethylcyclopentane 84.09 83.90 propylcyclohexane 84.99 86.47 1-nonene 85.18 87.13 1-decene 85.55 88.32 1-dodecene 85.92 89.47 1-tetradecene 86.41 85.14 cis-2-hexene 84.78 86.41 trans-2-hexene 86.41 84.52 cis-3-hexene 86.41 85.10 trans-3-hexene 84.32 84.11 2-methyl-1-pentene 83.90 82.19 3-methyl-1-pentene 83.90 82.78 4-methyl-1-pentene 86.30 85.17 2-methyl-2-pentene 82.89 81.70 4,4-dimethyl-l-pentene 85.95 84.98 2,4-dimethyl-2-pentene
1. 1-Methyl-1-ethylcyclopentane, Jsmol-l-K-l: CHz-CHp.
4(-CH2-) inring
+
+
(SC)
+
inring
=86.9178
+
(44
(-CH2-) connectedtoring
+
(-CHI) noming
J.moT’K‘
error: -0.96a/o
= 88.088 J*rnol-l*K-l:
m AS* = A +
E(&)
+
in aromatic ring
+
-1.92 -1.25 -1.95 -1.75 -1.95 -1.44 -1.27 -1.75 -1.30 -3.10 -2.00 -2.60 -2.29 -2.64 -3.42 -2.42 -1.97 -2.08 -1.01 -1.41 -0.90 -1.47 -0.88 -0.72 0.23 -1.71 -2.24 -3.14 -3.97 1.41 1.92 2.24 1.54 0.25 0.21 1.35 1.33 1.21 1.14
-cH3
mnededtoring
2. Naphthalene,
-0.11
= 84.115
+ q-0.43744) + 1.02830-1.48445 + 0.03176-1.43477
re3.309
error -2.16 -1.92 -1.53 -1.40
C ,HI
I
CH~-CH+CH~
AS* = A
5%
~
-86.9178 8(-0.08451) =87.939 J W ’ K ’ errw. -0.17%
2(=C)
in aromatic ring
no. 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88
exptl data, calcd data, compound J-mol-1.K-1 Jemol-1.K-1 3-methyl-2-ethyl-1-butene 84.26 83.97 1-methyl-2-propylbenzene 86.13 88.50 86.41 1-methyl-3-propylbenzene 88.50 85.78 1-methyl-4-propylbenene 88.50 85.02 1-methyl-2-isopropjlbenzene 86.50 1-methyl-3-isopropylbenzene 85.04 86.50 1-methyl-4-isopropylbenzene 84.75 86.50 l,2-diethylbenzene 86.32 88.72 1,3-diethylbenzene 88.72 86.67 l,4-diethylbenzene 86.17 88.72 94.15 1,2,3,4-tetramethylbenzene 89.37 1,2,3,5-tetramethylbenzene 92.98 89.37 1,2,4,5-tetramethylbenzene 96.97 89.37 pentylbenzene 86.19 88.12 87.25 1-pentanethiol 87.22 84.26 2-methyl-2-butanethiol 86.92 thiacyclopentane 87.86 90.06 86.31 thiacyclohexane 90.25 2-propenol 108.00 106.04 2-methyl-1-butanol 112.43 107.68 2,2-dimethyl-l-propanol 111.56 105.05 3-methyl-1-butanol 109.05 106.25 100.04 l-octanol 107.34 101.72 2-ethyl-1-hexanol 106.81 97.93 2-0ctan01 107.30 96.57 2,3-dimethylphenol 99.41 2,4-dimethylphenol 97.39 99.41 96.93 2,5-dimethylphenol 99.41 93.89 2,6-dimethylphenol 99.41 99.32 3,4-dimethylphenol 99.41 99.64 3,5-dimethylphenol 99.41 85.77 ethyl ethenyl ether 86.72 89.47 n-valeraldehyde 89.73 90.54 methyl acrylate 90.75 89.18 ethyl acrylate 90.94 91.26 methyl benzoate 92.08 92.14 ethyl benzoate 92.27 85.11 3-chloropropene 86.36 84.93 1,2-dichloropropane 86.59 1,2,3-trichloropropane 89.53 89.09 87.44 1,2-dichlorobenzene 86.89 86.59 1,3-dichlorobenzene 86.89 86.71 1,4-dichlorobenzene 86.89 93.81 morpholine 94.89 average absolute deviation
% error
-0.34 2.75 2.42 3.17 1.74 1.72 2.06 2.78 2.37 2.96 -5.08 -3.88 -7.84 2.24 0.03 3.16 2.50 4.56 -1.81 -4.22 -9.09 -2.67 7.30 5.00 9.30 2.94 2.07 2.56 5.88 0.09 -0.23 1.11 0.29 0.23 1.97 0.90 0.14 1.47 1.95 0.49 0.35 0.21 0.21 1.15 2.16
Literature Cited (1) Chen, N. H. Generalied Correlation for Latent Heat of Vaporization. J. Chem. Eng. Data 1965, 10, 207. (2) Giacalone, A. The Invariance of Heat of Vaporization with Temperature and the Theory of CorrespondingStates. Gozz. Chim. Ital. 1951,81, 180. (3) Hoshino, D.; Nagahama, K.; Hirata, M. Prediction of the Entropy of Vaporization at the Normal Boiling Point by the Group Contribution Method. Ind. Eng. Chem. Fundam. 1983,22,430. (4) Majer, V.; Svoboda,V. Enthalpies of Vaporization of Organic Compounds, A Critical Review and Data Compilation; Blackwell Scientific: Oxford, 1985. ( 5 ) Reid, R. C.; Prausnitz, J. M.; Polling, B. E. The Properties of Gases and Liquids, 4thed.; McGraw-Hilk New York, 1987;Appendix A Property Data Bank, p 656. (6) Riedel, L. Kritischer Koeffiiient, Dichte des Gesattigten Dampfes und Verdampfungswarme. Chem. Ing. Tech. 1954,26,679. (7) Shinoda, K. Principles of Solution and Solubility; Marcel Dekker: New York, 1978; p 8.
Received for review March 1, 1993 Revised manuscript received August 3, 1993 Accepted August 25, 1993.
+ 2(0.94853) Abstract published in Advance ACS Abstracts, October 15, 1993.
